Equilibrium Conditions and Evolution of Needle Domain Arrays in Ferroelectric Single Crystals

Experimental imaging of ferroelectric single crystals often reveals the formation of periodic arrays of needle-shaped domains of a compatible polarization variant coexisting with a homogeneous single domain parent variant. This study examines the far field electromechanical loading conditions that favor the formation, existence and evolution of compatible and stable needle domain array patterns using a phase-field modeling approach. The infinite arrays of needles are modeled via a representative unit cell and the appropriate electrical and mechanical periodic boundary conditions. A theoretical investigation of the generalized loading conditions is carried out to determine the sets of averaged loading states that lead to stationary needle tip locations. The resulting boundary value problems are solved using a non-linear finite element method to determine the details of the needle shape as well as the field distributions around the needle tips.